This is an important result, since it ensures that electromagnetic fields
do not change the rest mass of charged particles. In order to appreciate this,
let us assume that the rest mass is not a constant.
Since

(1566)

we can use the standard results
and
to give

(1567)

Thus, if rest mass is to remain an invariant, it is imperative that
all laws of physics predict 4-forces acting on particles which
are orthogonal to the particles' 4-velocities. The laws of electromagnetism
pass this test.